Finite Group Databasebeta

C2×#26044183 #37554174

order23488
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#26044183

Splittings

FittingC22×C8×C367 ⋊ C2
SylowC367 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23D1468
commutatorC4×C367C22×C4
FrattiniC2×C4C22×D367
FittingC22×C8×C367C2
socleC23×C367D4
prime radicalC22×D1468C2
cosocleC2×C4×C367C23
hypercenterC22×C8D367
hypocenterC367C2×#102
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 537);