Finite Group Databasebeta

C2×#27212373 #41003603

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

Aliases

direct productC2×#27212373

Splittings

SylowC421 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D421
commutatorC2×C421C23×C4
FrattiniC4C23×D421
Fitting, prime radicalC2×#41×C421C2
socleC22×C421C22×C4
cosocleC4×C421C24
hypercenterC2×#41D421
hypocenterC421C2×#131
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

4240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1312);