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D4×Q8×C211 #27212827

order13504
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C211 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C211

Subgroups

subgroupG/H
center, socleC22×C211C24
commutator, Frattini, cosocleC22C24×C211
prime radicalC2×D4×C211C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C211 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6752

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#41012501, #41012563, #41012647, …
maximal subgroup of#1627×C211, #1637×C211, #1649×C211, …
maximal normal subgroup of#1627×C211, #1637×C211, #1649×C211, …
maximal quotient ofQ8×C22⋊C4×C211, D4×C4⋊C4×C211, Q8×C4⋊C4×C211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 230);