Finite Group Databasebeta

C2×#26044204 #37554609

order23488
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#26044204

Splittings

FittingC2×Q16×C367 ⋊ C2
SylowC367 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#19154562
commutator, cosocleC8×C367C23
FrattiniC8C22×D367
FittingC2×Q16×C367C2
socleC22×C367D8
prime radicalC2×D2936C2
hypercenterC2×Q16D367
hypocenterC367C2×SD32
LCSG ▷ C8×C367 ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 972);