Finite Group Databasebeta

C2×#15692955 #20267825

order6592
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#15692955

Splittings

SylowC103 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D412
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
FittingC22×C8×C103C2
socleC23×C103D4
hypercenterC22×C8D103
hypocenterC103C2×#107
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#27193235, #27193236, #27193253, …
maximal normal subgroup of#27193235, #27193236, #27193253, …
maximal quotient ofC2×#20267544, #27193903, #27193919, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6592, 583);