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C4×C43×#3861 #38760360

order25284
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productC4×C43×#3861

Splittings

Fitting, HallC4×C72×C43 ⋊ C3
derived, SylowC72 ⋊ C3×C4×C43
HallC72×C43 ⋊ C3×C4
HallC4×C72 ⋊ C3×C43

Subgroups

subgroupG/H
center, hypercenterC4×C43#3861
commutator, hypocenterC72C3×C4×C43
FrattiniC2C2×C43×#3861
FittingC4×C72×C43C3
socleC2×C72×C43C2×C3
prime radicalC2×C43×#3861C2
cosocleC2×C72C2×C3×C43
LCSG ▷ C72
UCSC1 ◁ C4×C43

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8428

Conjugacy classes & character table

3268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 167);