Finite Group Databasebeta

C2×#27212454 #41003917

order26944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27212454

Splittings

SylowC421 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#13132997
commutatorC2×C421C23×C4
FrattiniC2C23×#13132997
FittingC2×Q8×C421C4
socleC22×C421C22×C4
prime radicalC2×#20269772C2
cosocleDic421C24
hypercenterC2×Q8#13132997
hypocenterC421C2×#131
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1626);