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D4×Q8×C269 #31770286

order17216
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C269

Subgroups

subgroupG/H
center, socleC22×C269C24
commutator, Frattini, cosocleC22C24×C269
prime radicalC2×D4×C269C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C269 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#46809988, #46810050, #46810134, …
maximal subgroup of#1627×C269, #1637×C269, #1649×C269, …
maximal normal subgroup of#1627×C269, #1637×C269, #1649×C269, …
maximal quotient ofQ8×C22⋊C4×C269, D4×C4⋊C4×C269, Q8×C4⋊C4×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 230);