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C23×#11761640 #22575542

order8608
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11761640
unambiguous semidirect productD269⋊(C22×C4)

Splittings

Fitting, socleC23×C269 ⋊ C4
derived, SylowC269 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11761640
commutator, hypocenterC269C23×C4
FrattiniC1G
Fitting, socleC23×C269C4
LCSG ▷ C269
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11761640)⋊C4, C22⋊C4×#11761640, #31771552, …
maximal normal subgroup ofC2×(C2×#11761640)⋊C4, C22⋊C4×#11761640, #31771552, …
maximal quotient ofC22×C4×#11761640, C22×C22⋊#11761640, C22×C4⋊#11761640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8608, 235);