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Q82×C211 #27212836

order13504
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C211 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C211

Subgroups

subgroupG/H
center, socle, prime radicalC22×C211C24
commutator, Frattini, cosocleC22C24×C211
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C211 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13504

Conjugacy classes & character table

5275 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41012476, #41012538, #41012619
maximal subgroup of#1623×C211, #1633×C211, #1645×C211, …
maximal normal subgroup of#1623×C211, #1633×C211, #1645×C211, …
maximal quotient ofQ8×C4⋊C4×C211, #2369×C211, #2451×C211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 239);