Finite Group Databasebeta

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C4⋊C4×D727 #37551501

order23264
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D727

Splittings

FittingC4⋊C4×C727 ⋊ C2
SylowC727 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D727
commutatorC2×C727C22×C4
FittingC4⋊C4×C727C2
socle, cosocleC22×C727C23
prime radicalC22×D727C22
hypercenterC4⋊C4D727
hypocenterC727C2×C4⋊C4
LCSG ▷ C2×C727 ▷ C727
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11632

Conjugacy classes & character table

3650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23264, 99);