Finite Group Databasebeta

C2×#27163020 #38762513

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

Aliases

direct productC2×#27163020

Splittings

SylowC397 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23C22⋊D397
commutatorC4×C397C22×C4
FrattiniC2×C4C22×D397
FittingC22×Q8×C397C2
socle, prime radicalC23×C397D4
cosocleC2×C4×C397C23
hypercenterC22×Q8D397
hypocenterC397C2×#103
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

162 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, 540);