Finite Group Databasebeta

← Prev (#27212832) Next (#27212834) →

#555×C211 #27212833

order13504
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C211 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C211

Subgroups

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

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6752

Conjugacy classes & character table

5275 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41012481, #41012543, #41012626
maximal subgroup of#1624×C211, #1634×C211, #1646×C211, …
maximal normal subgroup of#1624×C211, #1634×C211, #1646×C211, …
maximal quotient of#2346×C211, #2354×C211, #2363×C211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 236);