Finite Group Databasebeta

← Prev (#21440336) Next (#21440338) →

C4×C7×C11×C25 #21440337

order7700
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C3×C4×C52 (order 2400) · Inn(G) = C1 · Out(G) = C23×C3×C4×C52
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7700
abelianC4×C7×C11×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC2×C5C2×C5×C7×C11
socleC2×C5×C7×C11C2×C5
LCSG ▷ C1
UCSC1 ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7700 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic7700, D15400
Fitting subgroup ofC4×C11×ΓL(1,𝔽8)×C25
maximal subgroup ofC3×C4×C7×C11×C25, C4×C11×ΓL(1,𝔽8)×C25, C7×C11×Dic3×C25, …
maximal normal subgroup ofC3×C4×C7×C11×C25, C4×C11×ΓL(1,𝔽8)×C25, C7×C8×C11×C25, …
maximal quotient ofC3×C4×C7×C11×C25, C7×C11×Dic3×C25, C7×C8×C11×C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 1);