Finite Group Databasebeta

#534×C211 #27212812

order13504
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C211 · Schur multiplier (H2) = C25

Aliases

direct product#534×C211

Subgroups

subgroupG/H
center, socleC22×C211C24
commutator, Frattini, cosocleC22C24×C211
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C211 ◁ G

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3376

Conjugacy classes & character table

4642 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41012316, #41012350, #41012384, …
maximal subgroup of#1595×C211, #1601×C211, #1607×C211, …
maximal normal subgroup of#1595×C211, #1601×C211, #1607×C211, …
maximal quotient of#2308×C211, #2315×C211, #2321×C211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 215);