Finite Group Databasebeta

#555×C239 #29504459

order15296
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C239

Subgroups

subgroupG/H
center, socleC22×C239C24
commutator, Frattini, cosocleC22C24×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7648

Conjugacy classes & character table

5975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483631, #44483693, #44483776, …
maximal subgroup of#1624×C239, #1634×C239, #1646×C239, …
maximal normal subgroup of#1624×C239, #1634×C239, #1646×C239, …
maximal quotient of#2346×C239, #2354×C239, #2363×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 236);