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C4×C72×C43⋊C3 #38760361

order25284
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C72×C43⋊C3

Splittings

Fitting, HallC4×C72×C43 ⋊ C3
derived, SylowC43 ⋊ C3×C4×C72
HallC72×C43 ⋊ C3×C4
HallC4×C43 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC4×C72C43⋊C3
commutator, hypocenterC43C3×C4×C72
FrattiniC2C2×C72×C43⋊C3
FittingC4×C72×C43C3
socleC2×C72×C43C2×C3
prime radicalC2×C72×C43⋊C3C2
cosocleC2×C43C2×C3×C72
LCSG ▷ C43
UCSC1 ◁ C4×C72

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8428

Conjugacy classes & character table

3332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 168);