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C23×#13083549 #26033345

order11392
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC23×#13083549

Splittings

derived, SylowC89 ⋊ C23×C16

Subgroups

subgroupG/H
center, hypercenterC23×C8D89
commutator, hypocenterC89C23×C16
FrattiniC8C23×D89
FittingC23×C8×C89C2
socle, prime radicalC24×C89C8
cosocleC8×C89C24
LCSG ▷ C89
UCSC1 ◁ C23×C8

440 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#26018329, C2×#26018330, #36469271, …
maximal normal subgroup ofC2×#26018329, C2×#26018330, #36469271, …
maximal quotient ofC22×C4×#13083549, C22×C22⋊#13083549, C22×C4⋊#13083549, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 17603);