Finite Group Databasebeta

C2×#103×D227 #44408222

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#103×D227

Splittings

FittingC2×#103×C227 ⋊ C2
SylowC227 ⋊ C22×#103

Subgroups

subgroupG/H
centerC23D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC2×#103×C227C2
socleC23×C227C2×D4
prime radicalC23×D227D4
cosocleC2×C4×C227C24
hypercenterC2×#103D227
hypocenterC227C22×#103
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12998);