Finite Group Databasebeta

C8×Dic458 #28411606

order14656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic458

Splittings

SylowC229 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D229
commutatorC2×C229C22×C8
FrattiniC2×C4C22×D229
FittingC4×C8×C229C2
socle, prime radicalC22×C229C22×C4
cosocleC2×C4×C229C23
hypercenterC4×C8D229
hypocenterC229C8×Q8
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C2×C8 ◁ C4×C8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 674);