Finite Group Databasebeta

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C2×C4×C5×C193 #72186641

order7720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C5×C193
multiplicative(ℤ/8503)ˣ, (ℤ/9655)ˣ, (ℤ/17006)ˣ, (ℤ/19310)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C5×C193
socle, prime radicalC22×C5×C193C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C5×C193, C2×C5×C8×C193, C22×C4×C5×C193, …
maximal normal subgroup ofC42×C5×C193, C2×C5×C8×C193, C22×C4×C5×C193, …
maximal quotient ofC42×C5×C193, C2×C5×C8×C193, C22×C4×C5×C193, …
automorphism group ofC11×C773, C5×C1931
outer automorphism group ofC11×C773, C5×C1931

GAP

Past the SmallGroups library coverage — no SmallGroups id.