Finite Group Databasebeta

C2×#27163025 #38762542

order25408
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27163025

Splittings

SylowC397 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D397
commutatorC2×C397C22×C8
FrattiniC2×C4C22×D397
FittingC22×C8×C397C2
socle, prime radicalC23×C397C2×C4
cosocleC2×C4×C397C23
hypercenterC22×C8D397
hypocenterC397C2×C4⋊C8
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C22×C4 ◁ C22×C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

6376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 569);