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D4×Q8×C293 #34035810

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
prime radicalC2×D4×C293C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

7325 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49157888, #49157950, #49158034, …
maximal subgroup of#1627×C293, #1637×C293, #1649×C293, …
maximal normal subgroup of#1627×C293, #1637×C293, #1649×C293, …
maximal quotient ofQ8×C22⋊C4×C293, D4×C4⋊C4×C293, Q8×C4⋊C4×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 230);