Finite Group Databasebeta

D8×Dic593 #49182798

order37952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic593

Splittings

SylowC593 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D593
commutatorC4×C593C22×C4
FrattiniC2×C4C22×D593
Fitting, prime radicalC2×D8×C593C2
socleC22×C593C2×D4
cosocleC2×C4×C593C23
hypercenterC2×D8D593
hypocenterC593C4×D8
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

4172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 632);