Finite Group Databasebeta

#534×C227 #28408698

order14528
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C227 · Schur multiplier (H2) = C25

Aliases

direct product#534×C227

Subgroups

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

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

Conjugacy classes & character table

4994 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44398652, #44398686, #44398720, …
maximal subgroup of#1595×C227, #1601×C227, #1607×C227, …
maximal normal subgroup of#1595×C227, #1601×C227, #1607×C227, …
maximal quotient of#2308×C227, #2315×C227, #2321×C227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14528, 215);