Finite Group Databasebeta

#555×C227 #28408719

order14528
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C227 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C227

Subgroups

subgroupG/H
center, socleC22×C227C24
commutator, Frattini, cosocleC22C24×C227
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C227 ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

5675 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44398817, #44398879, #44398962, …
maximal subgroup of#1624×C227, #1634×C227, #1646×C227, …
maximal normal subgroup of#1624×C227, #1634×C227, #1646×C227, …
maximal quotient of#2346×C227, #2354×C227, #2363×C227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14528, 236);