Finite Group Databasebeta

C2×#27163031 #38762567

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

Aliases

direct productC2×#27163031

Splittings

SylowC397 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D397
commutatorC4×C397C22×C4
FrattiniC2×C4C22×D397
FittingC2×M16×C397C2
socleC22×C397C4⋊C4
prime radicalC23×C397Q8
cosocleC2×C4×C397C23
hypercenterC2×M16D397
hypocenterC397C2×#108
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

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, 594);