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C2×C3×C7×C11×C25 #26040437

order11550
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11550
abelianC2×C3×C7×C11×C25
multiplicative(ℤ/11551)ˣ, (ℤ/23102)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C2×C3×C5×C7×C11
socle, prime radicalC2×C3×C5×C7×C11C5
LCSG ▷ C1
UCSC1 ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11550 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11550, D23100
Fitting subgroup ofC3×C7×C25×Dic11, C3×C11×C25×Dic7, C3×C25×Dic77, …
maximal subgroup ofC3×C4×C7×C11×C25, C3×C7×C25×Dic11, C3×C11×C25×Dic7, …
maximal normal subgroup ofC3×C4×C7×C11×C25, C3×C7×C25×Dic11, C3×C11×C25×Dic7, …
maximal quotient ofC3×C4×C7×C11×C25, C22×C3×C7×C11×C25, C2×C7×C9×C11×C25, …
automorphism group ofC11551
outer automorphism group ofC11551

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 1);