Finite Group Databasebeta

← Prev (#27165393) Next (#27165395) →

C11×C22⋊(C97⋊C3) #27165394

order12804
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊(C97⋊C3)
unambiguous semidirect productC22⋊(C11×C97⋊C3)
unambiguous semidirect product(C22×C11)⋊(C97⋊C3)
unambiguous semidirect productC97⋊(C11×A4)
unambiguous semidirect product(C11×C97)⋊A4

Splittings

Fitting, socle, HallC22×C11×C97 ⋊ C3
derived, HallC22×C97 ⋊ C3×C11
HallC11×C97 ⋊ A4
SylowC97 ⋊ C11×A4
HallC22×C11 ⋊ C97⋊C3
SylowC22 ⋊ C11×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C22⋊(C97⋊C3)
commutator, cosocle, hypocenterC22×C97C3×C11
FrattiniC1G
Fitting, socleC22×C11×C97C3
LCSG ▷ C22×C97
UCSC1 ◁ C11

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 112
transitive degreeμt(G) = 4268

A minimal faithful permutation representation — 2 generators on 112 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,59)(41,55,66)(44,58,63)(47,61,60)(50,64,57)(52,67,54)(56,71,73)(62,75,77)(65,78,74)(68,80,72)(69,76,70)(79,86,85)(81,88,84)(82,87,83)(89,93,92)(90,94,91)(95,97,96)(99,100,101)(102,103,104,105,106,107,108,109,110,111,112);(1,2,4,8,15,25,38,40,14,23,34,47,62,76,51,66,53,69,82,90,95,97,88,64,33,12,19,29,42,57,72,83,75,43,17,3,6,11,18,28,41,56,55,24,36,50,65,79,87,67,35,48,63,77,85,92,96,93,78,46,20,5,9,16,26,39,54,70,58,27,7,13,21,31,44,59,73,71,37,52,68,81,89,94,80,49,22,32,45,60,74,84,91,86,61,30,10)(98,101)(99,100)

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×A4×C97⋊C3, C3×C11×C22⋊(C97⋊C3)
maximal normal subgroup ofC11×A4×C97⋊C3, C3×C11×C22⋊(C97⋊C3)
maximal quotient ofC11×C22⋊(C97⋊C9), C3×C11×C22⋊(C97⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12804, 31);