Finite Group Databasebeta

C2×#26044217 #37554639

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#26044217

Splittings

SylowC367 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D367
commutatorC2×C367C23×C4
FrattiniC22C23×D367
FittingC2×C22⋊C4×C367C2
socleC23×C367C23
prime radicalC24×C367C22
cosocleC22×C367C24
hypercenterC2×C22⋊C4D367
hypocenterC367C2×#117
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1002);