Finite Group Databasebeta

D8×Dic409 #39909330

order26176
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic409

Splittings

SylowC409 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D409
commutatorC4×C409C22×C4
FrattiniC2×C4C22×D409
Fitting, prime radicalC2×D8×C409C2
socleC22×C409C2×D4
cosocleC2×C4×C409C23
hypercenterC2×D8D409
hypocenterC409C4×D8
LCSG ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

2884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 632);