Finite Group Databasebeta

#418×D227 #44408232

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

Aliases

direct product#418×D227

Splittings

Fitting#418×C227 ⋊ C2
SylowC227 ⋊ C2×#418

Subgroups

subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
Fitting#418×C227C2
socleC22×C227C22×D4
prime radicalC22×D4×D227C2
cosocleC2×C4×C227C24
hypercenter#418D227
hypocenterC227C2×#418
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13008);