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C23×#11929411 #23756586

order10016
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11929411
unambiguous semidirect productD313⋊(C22×C4)

Splittings

Fitting, socleC23×C313 ⋊ C4
derived, SylowC313 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11929411
commutator, hypocenterC313C23×C4
FrattiniC1G
Fitting, socleC23×C313C4
prime radicalC23×D313C2
cosocleD313C24
LCSG ▷ C313
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11929411)⋊C4, C22⋊C4×#11929411, #34095099, …
maximal normal subgroup ofC2×(C2×#11929411)⋊C4, C22⋊C4×#11929411, #34095099, …
maximal quotient ofC22×C4×#11929411, C22×C22⋊#11929411, C22×C4⋊#11929411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10016, 235);