Finite Group Databasebeta

C2×#32914738 #49149004

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

Aliases

direct productC2×#32914738

Splittings

SylowC577 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#14556313
commutatorC2×C577C22×C8
FrattiniC4C22×#14556313
FittingC22×C4×C577C4
socleC22×C577C2×C8
prime radicalC23×C577C8
cosocle#17987230C23
hypercenterC22×C4#14556313
hypocenterC577C2×M32
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C2×C4 ◁ C22×C4

90 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, 1604);