Finite Group Databasebeta

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C2×C4×C25×C64 #72191111

order12800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 327680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C25×C64
multiplicative(ℤ/24015)ˣ, (ℤ/25616)ˣ, (ℤ/25856)ˣ, (ℤ/32000)ˣ, (ℤ/32020)ˣ, (ℤ/48030)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5×C32C23×C5
socle, prime radicalC23×C5C2×C5×C32
LCSG ▷ C1
UCSC1 ◁ G

486 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C25×C128, C2×C8×C25×C64, C42×C25×C64, …
maximal normal subgroup ofC2×C4×C25×C128, C2×C8×C25×C64, C42×C25×C64, …
maximal quotient ofC2×C4×C25×C128, C2×C8×C25×C64, C42×C25×C64, …
automorphism group ofC125×C256
outer automorphism group ofC125×C256

GAP

Past the SmallGroups library coverage — no SmallGroups id.