Finite Group Databasebeta

C2×#27163014 #38762501

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27163014

Splittings

SylowC397 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#20263708
commutatorC22×C397C22×C4
FrattiniC2×C4C22×D397
FittingC2×M16×C397C2
socleC22×C397C22⋊C4
prime radicalC23×C397C2×C4
cosocleC2×C4×C397C23
hypercenterC2×M16D397
hypocenterC397C2×#101
LCSG ▷ C22×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

3982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 528);