Finite Group Databasebeta

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C2×C5×C16×C101 #72194128

order16160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 12800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C16×C101
multiplicative(ℤ/24243)ˣ, (ℤ/32324)ˣ, (ℤ/48486)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C5×C101
socle, prime radicalC22×C5×C101C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C32×C101, C4×C5×C16×C101, C22×C5×C16×C101
maximal normal subgroup ofC2×C5×C32×C101, C4×C5×C16×C101, C22×C5×C16×C101
maximal quotient ofC2×C5×C32×C101, C4×C5×C16×C101, C22×C5×C16×C101

GAP

Past the SmallGroups library coverage — no SmallGroups id.