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#585×C157 #23756990

order10048
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C157 · Schur multiplier (H2) = C29

Aliases

direct product#585×C157

Subgroups

subgroupG/H
centerC4×C157C24
commutator, Frattini, cosocleC2C25×C157
socleC2×C157C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C157 ◁ G

810 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5338 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#1791×C157, #1794×C157, #2901×C157, …
maximal normal subgroup of#1791×C157, #1794×C157, #2901×C157, …
maximal quotient of#3428×C157, C4×H(5,𝔽2)×C157, C4×2−1+4×C157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 266);