Finite Group Databasebeta

C2×#10624985 #13092366

order1472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#10624985

Splittings

SylowC23 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D23
commutatorC2×C23C2×C42
FrattiniC2×C4C22×D23
FittingC2×C42×C23C2
socle, prime radicalC23×C23C2×C4
cosocleC2×C4×C23C23
hypercenterC2×C42D23
hypocenterC23C2×#97
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C42

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

Relationships

maximal subgroup of#15671227, #15671241, #15671278, …
maximal normal subgroup of#15671227, #15671241, #15671278, …
maximal quotient ofC2×#13092139, #15671684, #15671689, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 498);