Finite Group Databasebeta

#550×C199 #27163700

order12736
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C199 · Schur multiplier (H2) = C25

Aliases

direct product#550×C199

Subgroups

subgroupG/H
center, socleC22×C199C24
commutator, Frattini, cosocleC22C24×C199
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C199 ◁ G

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6368

Conjugacy classes & character table

4975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38767915, #38767977, #38768043, …
maximal subgroup of#1621×C199, #1631×C199, #1641×C199, …
maximal normal subgroup of#1621×C199, #1631×C199, #1641×C199, …
maximal quotient of#2341×C199, Q8×C4⋊C4×C199, #2354×C199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12736, 231);