Finite Group Databasebeta

← Prev (#27166386) Next (#27166388) →

C4×C43×C52⋊C3 #27166387

order12900
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C5

Aliases

direct productC4×C43×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C43)

Splittings

Fitting, HallC4×C52×C43 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C43
HallC52×C43 ⋊ C3×C4
HallC4×C52 ⋊ C3×C43

Subgroups

subgroupG/H
center, hypercenterC4×C43C52⋊C3
commutator, hypocenterC52C3×C4×C43
FrattiniC2C2×C43×C52⋊C3
FittingC4×C52×C43C3
socleC2×C52×C43C2×C3
prime radicalC2×C43×C52⋊C3C2
cosocleC2×C52C2×C3×C43
LCSG ▷ C52
UCSC1 ◁ C4×C43

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 2580

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,4)(3,7,9)(5,10,13)(6,12,15)(8,11,14)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)(59,60,61,62);(1,3,8,13,15)(2,7,11,5,6)(4,10,9,12,14)

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 56);