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C4⋊C8×D223 #28383599

order14272
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D223

Splittings

FittingC4⋊C8×C223 ⋊ C2
SylowC223 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D223
commutatorC2×C223C22×C8
FittingC4⋊C8×C223C2
socleC22×C223C22×C4
prime radicalC22×D223C2×C4
cosocleC2×C4×C223C23
hypercenterC4⋊C8D223
hypocenterC223C2×C4⋊C8
LCSG ▷ C2×C223 ▷ C223
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7136

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14272, 568);