Finite Group Databasebeta

C2×C4⋊C8×D293 #49167334

order37504
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4⋊C8×D293

Splittings

FittingC2×C4⋊C8×C293 ⋊ C2
SylowC293 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D293
commutatorC2×C293C23×C8
FrattiniC2×C4C23×D293
FittingC2×C4⋊C8×C293C2
socleC23×C293C22×C4
prime radicalC23×D293C2×C4
cosocleC2×C4×C293C24
hypercenterC2×C4⋊C8D293
hypocenterC293C22×C4⋊C8
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 13059);