Finite Group Databasebeta

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C2×C32×C5×C8×C19 #72191887

order13680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C5×C8×C19
multiplicative(ℤ/14167)ˣ, (ℤ/15967)ˣ, (ℤ/20529)ˣ, (ℤ/28334)ˣ, (ℤ/31934)ˣ, (ℤ/41058)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C32×C5×C19
socle, prime radicalC22×C32×C5×C19C4
LCSG ▷ C1
UCSC1 ◁ G

264 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C5×C16×C19, C32×C4×C5×C8×C19, C22×C32×C5×C8×C19
maximal normal subgroup ofC2×C32×C5×C16×C19, C32×C4×C5×C8×C19, C22×C32×C5×C8×C19
maximal quotient ofC2×C32×C5×C16×C19, C32×C4×C5×C8×C19, C22×C32×C5×C8×C19
automorphism group ofC31×C457, C7×C2281
outer automorphism group ofC31×C457, C7×C2281

GAP

Past the SmallGroups library coverage — no SmallGroups id.