Finite Group Databasebeta

C4×#20263732 #38762992

order25408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#20263732

Splittings

FittingC4×Q8×C397 ⋊ C2
SylowC397 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D397
commutatorC2×C397C23×C4
FrattiniC22C23×D397
FittingC4×Q8×C397C2
socle, cosocleC22×C397C24
prime radicalC2×#20263732C2
hypercenterC4×Q8D397
hypocenterC397C4×#41
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C4×Q8

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1019);