Finite Group Databasebeta

C2×C22⋊(C367⋊C8) #37554147

order23488
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊(C367⋊C8)

Splittings

SylowC367 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D367
commutatorC2×C367C22×C8
FrattiniC2×C4C22×D367
FittingC23×C4×C367C2
socleC23×C367C2×C4
prime radicalC24×C367C4
cosocleC2×C4×C367C23
hypercenterC23×C4D367
hypocenterC367C2×C22⋊C8
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 510);