Finite Group Databasebeta

#410×D227 #44408188

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

Aliases

direct product#410×D227

Splittings

Fitting#410×C227 ⋊ C2
SylowC227 ⋊ C2×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
Fitting#410×C227C2
socleC2×C227C22×C22⋊C4
prime radicalC2×#41×D227C2
cosocleC23×C227C24
hypercenter#410D227
hypocenterC227C2×#410
LCSG ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

788 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, 12964);