Finite Group Databasebeta

C2×#32914599 #49147994

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

Aliases

direct productC2×#32914599

Splittings

SylowC577 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D577
commutatorC4×C577C22×C4
FrattiniC2×C4C22×D577
FittingC2×M16×C577C2
socleC22×C577C4⋊C4
prime radicalC23×C577Q8
cosocleC2×C4×C577C23
hypercenterC2×M16D577
hypocenterC577C2×#108
LCSG ▷ C4×C577 ▷ C2×C577 ▷ C577
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18464

Conjugacy classes & character table

5788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 594);