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Q82×C269 #31770295

order17216
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C269

Subgroups

subgroupG/H
center, socle, prime radicalC22×C269C24
commutator, Frattini, cosocleC22C24×C269
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C269 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

6725 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46809963, #46810025, #46810106, …
maximal subgroup of#1623×C269, #1633×C269, #1645×C269, …
maximal normal subgroup of#1623×C269, #1633×C269, #1645×C269, …
maximal quotient ofQ8×C4⋊C4×C269, #2369×C269, #2451×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 239);