Finite Group Databasebeta

C2×C4×#17987237 #49148904

order36928
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#17987237

Splittings

derived, SylowC577 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#14556313
commutator, hypocenterC577C2×C4×C8
FrattiniC22C22×#14556313
FittingC22×C4×C577C4
socle, prime radicalC23×C577C2×C4
cosocleC2×Dic577C23
LCSG ▷ C577
UCSC1 ◁ C22×C4

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36928

Conjugacy classes & character table

2368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1504);