Finite Group Databasebeta

C2×#26044284 #37554969

order23488
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26044284

Splittings

FittingC2×Q16×C367 ⋊ C2
SylowC367 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D367
commutator, cosocleC4×C367C24
FrattiniC4C23×D367
FittingC2×Q16×C367C2
socleC22×C367C2×D4
hypercenterC2×Q16D367
hypocenterC367C2×#135
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

2590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1332);