Finite Group Databasebeta

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C22⋊C4×#10621902 #25255800

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22⋊C4×#10621902

Splittings

FittingQ8×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingQ8×C22⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC23×#10621902C2
hypercenterQ8×C22⋊C4D43
hypocenterC43C22⋊C4×#41
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328771);