Finite Group Databasebeta

C5×C1459 #20300451

order7295
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C729 (order 5832) · Inn(G) = C1 · Out(G) = C2×C4×C729
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7295
abelianC5×C1459

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7295 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7295, Dic7295, C1459⋊AGL(1,𝔽5), …
Fitting subgroup ofD5×C1459, C5×D1459, D7295, …
socle ofD5×C1459, C5×D1459, D7295, …
maximal subgroup ofD5×C1459, C5×D1459, D7295, …
maximal normal subgroup ofD5×C1459, C5×D1459, D7295, …
maximal quotient ofC2×C5×C1459, C3×C5×C1459, C25×C1459, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7295, 1);