Finite Group Databasebeta

C2×#27212323 #41003294

order26944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#27212323

Splittings

FittingC2×C42×C421 ⋊ C2
SylowC421 ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×D421
commutatorC2×C421C23×C4
FrattiniC22C23×D421
FittingC2×C42×C421C2
socleC23×C421C23
prime radicalC23×D421C22
cosocleC22×C421C24
hypercenterC2×C42D421
hypocenterC421C2×#117
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C22×C4 ◁ C2×C42

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

6760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1003);