Finite Group Databasebeta

C2×#27212273 #41002684

order26944
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27212273

Splittings

SylowC421 ⋊ C2×#95

Subgroups

subgroupG/H
centerC24C2×D421
commutatorC2×C421C2×C42
FrattiniC23C22×D421
FittingC23×C4×C421C2
socle, prime radicalC24×C421C22
cosocleC23×C421C23
hypercenterC23×C4D421
hypocenterC421C2×#95
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C24 ◁ C23×C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26944

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, 393);