Finite Group Databasebeta

#550×C239 #29504454

order15296
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C25

Aliases

direct product#550×C239

Subgroups

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

312 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#44483613, #44483675, #44483741, …
maximal subgroup of#1621×C239, #1631×C239, #1641×C239, …
maximal normal subgroup of#1621×C239, #1631×C239, #1641×C239, …
maximal quotient of#2341×C239, Q8×C4⋊C4×C239, #2354×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 231);