Finite Group Databasebeta

C2×#28409103 #44408413

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28409103

Splittings

FittingC23×C8×C227 ⋊ C2
SylowC227 ⋊ C2×#435

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC22×C227C23×C4
FrattiniC2×C4C23×D227
FittingC23×C8×C227C2
socleC23×C227C22×C4
prime radicalC22×C22⋊D227C4
cosocleC2×C4×C227C24
hypercenterC23×C8D227
hypocenterC227C2×#435
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C23×C8

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13189);