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C112×C3⋊(ΓL(1,𝔽8)⋊C4) #44479018

order30492
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC112×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(C112×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(C112×Dic3)
unambiguous semidirect productDic21⋊(C3×C112)
unambiguous semidirect product(C11×Dic21)⋊(C3×C11)

Splittings

derivedC3×C7 ⋊ C3×C4×C112
HallC3×C112×ΓL(1,𝔽8) ⋊ C4
HallC7×C112 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C112
SylowC7 ⋊ C3×C112×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C112C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C112
FrattiniC2C112×C3⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C112×ΓL(1,𝔽8)C2
cosocleC2×C3×C7C2×C3×C112
LCSG ▷ C3×C7
UCSC1 ◁ C2×C112

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10164

Conjugacy classes & character table

2904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 241);