Finite Group Databasebeta

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C25×C4×C5×C13 #72187248

order8320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 982977085440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C215

Aliases

abelianC25×C4×C5×C13

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C5×C13
socle, prime radicalC26×C5×C13C2
LCSG ▷ C1
UCSC1 ◁ G

21104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C5×C8×C13, C24×C42×C5×C13, C26×C4×C5×C13, …
maximal normal subgroup ofC25×C5×C8×C13, C24×C42×C5×C13, C26×C4×C5×C13, …
maximal quotient ofC25×C5×C8×C13, C24×C42×C5×C13, C26×C4×C5×C13, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.