Finite Group Databasebeta

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C4⋊C4×Dic172 #25115030

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic172

Splittings

SylowC43 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC8×C4⋊C4×C43C2
socle, prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC8×C4⋊C4D43
hypocenterC43C4⋊C4×Q16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 188001);