Finite Group Databasebeta

C4×#20263721 #38762615

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×#20263721

Splittings

SylowC397 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4C22⋊D397
commutatorC4×C397C22×C4
FrattiniC2×C4C22×D397
FittingC4×Q8×C397C2
socle, prime radicalC22×C397C2×D4
cosocleC2×C4×C397C23
hypercenterC4×Q8D397
hypocenterC397C4×Q16
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

3988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 642);