Finite Group Databasebeta

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C4⋊C4×#10621898 #25255912

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4⋊C4×#10621898

Splittings

FittingC2×C4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C4⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC22×#10621898C22
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C4⋊C4×#41
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

3250 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328883);