Finite Group Databasebeta

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C4⋊C8×D373 #37559441

order23872
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D373

Splittings

FittingC4⋊C8×C373 ⋊ C2
SylowC373 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D373
commutatorC2×C373C22×C8
FittingC4⋊C8×C373C2
socleC22×C373C22×C4
prime radicalC22×D373C2×C4
cosocleC2×C4×C373C23
hypercenterC4⋊C8D373
hypocenterC373C2×C4⋊C8
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

3760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 568);