Finite Group Databasebeta

C2×#27212357 #41003361

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

Aliases

direct productC2×#27212357

Splittings

SylowC421 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D421
commutator, cosocleC22×C421C24
FrattiniC22C23×D421
FittingC2×C4⋊C4×C421C2
socle, prime radicalC23×C421C23
hypercenterC2×C4⋊C4D421
hypocenterC421C2×#125
LCSG ▷ C22×C421 ▷ C421
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26944

Conjugacy classes & character table

4228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1070);