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C4×C72×ΓL(1,𝔽32) #44477134

order30380
automorphism?
homologyAbelianization (H1) = C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C72×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C31)⋊(C5×C72)
unambiguous semidirect product(C4×C7×C31)⋊(C5×C7)
unambiguous semidirect product(C4×C72×C31)⋊C5

Splittings

Fitting, HallC4×C72×C31 ⋊ C5
derived, SylowC31 ⋊ C4×C5×C72
HallC72×C31 ⋊ C4×C5
HallC4×C31 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC4×C72ΓL(1,𝔽32)
commutator, hypocenterC31C4×C5×C72
FrattiniC2C2×C72×ΓL(1,𝔽32)
FittingC4×C72×C31C5
socleC2×C72×C31C2×C5
prime radicalC2×C72×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C72
LCSG ▷ C31
UCSC1 ◁ C4×C72

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6076

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 43);