Finite Group Databasebeta

C2×Dic3176 #38762950

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

Aliases

direct productC2×Dic3176

Splittings

SylowC397 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3176
commutator, cosocleC8×C397C23
FrattiniC8C22×D397
FittingC2×C16×C397C2
socle, prime radicalC22×C397D8
hypercenterC2×C16D397
hypocenterC397C2×Q32
LCSG ▷ C8×C397 ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25408

Conjugacy classes & character table

6358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 977);