Finite Group Databasebeta

C2×C4×Dic818 #39909712

order26176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic818

Splittings

SylowC409 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D409
commutatorC2×C409C23×C4
FrattiniC22C23×D409
FittingC2×C42×C409C2
socle, prime radicalC23×C409C23
cosocleC22×C409C24
hypercenterC2×C42D409
hypocenterC409C2×C4×Q8
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26176

Conjugacy classes & character table

6568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 1014);