Finite Group Databasebeta

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C23×(C22⋊D43)⋊C4 #26003159

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×(C22⋊D43)⋊C4

Splittings

FittingC23×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC23×C22⋊C4×C43C2
socleC25×C43C23
prime radicalC24×C22⋊D43C2
cosocleC22×C43C26
hypercenterC23×C22⋊C4D43
hypocenterC43C23×C4×D4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C23×C22⋊C4

19998 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076130);