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C23×#11929639 #23778869

order10144
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11929639
unambiguous semidirect productD317⋊(C22×C4)

Splittings

Fitting, socleC23×C317 ⋊ C4
derived, SylowC317 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11929639
commutator, hypocenterC317C23×C4
FrattiniC1G
Fitting, socleC23×C317C4
prime radicalC23×D317C2
cosocleD317C24
LCSG ▷ C317
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

664 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11929639)⋊C4, C22⋊C4×#11929639, #35204170, …
maximal normal subgroup ofC2×(C2×#11929639)⋊C4, C22⋊C4×#11929639, #35204170, …
maximal quotient ofC22×C4×#11929639, C22×C22⋊#11929639, C22×C4⋊#11929639, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10144, 235);