Finite Group Databasebeta

C2×C22⋊#17987237 #49148916

order36928
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#17987237

Splittings

SylowC577 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#14556313
commutatorC2×C577C22×C8
FrattiniC22C22×#14556313
Fitting, prime radicalC24×C577C4
socleC23×C577C2×C4
cosocleC2×Dic577C23
hypercenterC24#14556313
hypocenterC577C2×C22⋊C8
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C23 ◁ C24

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

2344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1516);