Finite Group Databasebeta

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C7×C3⋊(C3⋊(C11⋊Dic11)) #44479037

order30492
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3×C11

Aliases

direct productC7×C3⋊(C3⋊(C11⋊Dic11))
unambiguous semidirect productC3⋊(C7×C3⋊(C11⋊Dic11))
unambiguous semidirect productC11⋊(C7×C3⋊Dic33)

Splittings

derived, HallC32×C112 ⋊ C4×C7
HallC32×C7×C112 ⋊ C4
HallC7×C112 ⋊ C3⋊Dic3
SylowC112 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C11⋊Dic11
SylowC32 ⋊ C7×C11⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C3⋊(C11⋊D11))
commutator, hypocenterC32×C112C4×C7
FrattiniC2C7×C3⋊(C3⋊(C11⋊D11))
Fitting, socle, prime radicalC2×C32×C7×C112C2
cosocleC2×C32×C112C2×C7
LCSG ▷ C32×C112
UCSC1 ◁ C2×C7

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 30492

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7)(9,10)(12,13)(14,15,16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(30,31)(32,33)(34,35)(36,37)(38,39);(11,12,13)(29,30,32,34,36,38,39,37,35,33,31);(8,9,10)(18,19,21,23,25,27,28,26,24,22,20)

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 260);