Finite Group Databasebeta

C8×Dic758 #37565369

order24256
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic758

Splittings

SylowC379 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D379
commutatorC2×C379C22×C8
FrattiniC2×C4C22×D379
FittingC4×C8×C379C2
socle, prime radicalC22×C379C22×C4
cosocleC2×C4×C379C23
hypercenterC4×C8D379
hypocenterC379C8×Q8
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C2×C8 ◁ C4×C8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24256

Conjugacy classes & character table

6088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 674);